Effective normal basis theorem
Number Theory
2026-01-22 v1
Abstract
Let K be a finite Galois extension of Q. The normal basis theorem provides an element of K whose conjugates form a Q-basis of K. Here we obtain such an element with controlled size. This improves a recent result by Fukshansky and Jeong. By the way, we estimate Minkowski's minima of ideals of integers of number fields.
Cite
@article{arxiv.2601.14856,
title = {Effective normal basis theorem},
author = {Pascal Autissier},
journal= {arXiv preprint arXiv:2601.14856},
year = {2026}
}
Comments
in French language